|Mar3-09, 02:05 AM||#1|
The Expectation of X and the Expectation of X squared (discrete math)
1. The problem statement, all variables and given/known data
prove or disprove that E[X^2] = E(X)^2
2. Relevant equations
E[X] = [tex]\sum[/tex]xi*pr(xi)
3. The attempt at a solution
I really don't know where to start, I believe that it is not true, so I should try to disprove it, and the easiest way to do that would be by counterexample... I don't understand expectation very well though, I could try to do a mathematical proof to show that they are not equal, but I don't know how to go about that either.
|Mar3-09, 02:27 AM||#2|
hi sammC - this is ripe for a counter example...
easiest would be to try a distribution with only 2 outcomes, ie 50% probability of each occurring, then calculate E[x] and E[X^2]
note E[X^2] = sum over i of pr(xi)*(xi^2)
|Mar3-09, 02:53 AM||#3|
ah, this helps a bunch, thanks!
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